DECAY PROPERTIES OF SOLUTIONS TO THE LINEARIZED COMPRESSIBLE NAVIER–STOKES EQUATION AROUND TIME-PERIODIC PARALLEL FLOW

Decay estimates on solutions to the linearized compressible Navier–Stokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L2 norm as an (n - 1)-dimensional heat kernel. Furthermore, it is proved that the asymptotic leading part of solutions is given by solutions of an (n - 1)-dimensional linear heat equation with a convective term multiplied by time-periodic function.

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Spectral properties of the linearized compressible Navier–Stokes equation around time-periodic parallel flow

Journal of Differential Equations ◽

10.1016/j.jde.2013.04.036 ◽

2013 ◽

Vol 255 (6) ◽

pp. 1132-1195 ◽

Cited By ~ 12

Author(s):

Jan Březina ◽

Yoshiyuki Kagei

Keyword(s):

Stokes Equation ◽

Spectral Properties ◽

Parallel Flow ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Time Periodic

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Asymptotic Behavior of Solutions to the Compressible Navier--Stokes Equation Around a Time-Periodic Parallel Flow

SIAM Journal on Mathematical Analysis ◽

10.1137/12089555x ◽

2013 ◽

Vol 45 (6) ◽

pp. 3514-3574 ◽

Cited By ~ 7

Author(s):

Jan Březina

Keyword(s):

Asymptotic Behavior ◽

Stokes Equation ◽

Parallel Flow ◽

Navier Stokes ◽

Asymptotic Behavior Of Solutions ◽

Navier Stokes Equation ◽

Time Periodic

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DECAY ESTIMATES ON SOLUTIONS OF THE LINEARIZED COMPRESSIBLE NAVIER-STOKES EQUATION AROUND A PARALLEL FLOW IN A CYLINDRICAL DOMAIN

Kyushu Journal of Mathematics ◽

10.2206/kyushujm.69.293 ◽

2015 ◽

Vol 69 (2) ◽

pp. 293-343 ◽

Cited By ~ 4

Author(s):

Reika AOYAMA

Keyword(s):

Stokes Equation ◽

Parallel Flow ◽

Navier Stokes ◽

Cylindrical Domain ◽

Decay Estimates ◽

Navier Stokes Equation

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Time periodic strong solutions to the Keller-Segel system coupled to Navier-Stokes equation

Journal of Differential Equations ◽

10.1016/j.jde.2021.06.044 ◽

2021 ◽

Vol 298 ◽

pp. 95-131

Author(s):

Zhong Tan ◽

Zhonger Wu

Keyword(s):

Stokes Equation ◽

Strong Solutions ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Time Periodic

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Asymptotic Behavior of Solutions to the Compressible Navier–Stokes Equation Around a Parallel Flow

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-012-0516-5 ◽

2012 ◽

Vol 205 (2) ◽

pp. 585-650 ◽

Cited By ~ 22

Author(s):

Yoshiyuki Kagei

Keyword(s):

Asymptotic Behavior ◽

Stokes Equation ◽

Parallel Flow ◽

Navier Stokes ◽

Asymptotic Behavior Of Solutions ◽

Navier Stokes Equation

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Stability of time periodic solution of the Navier–Stokes equation on the half-space under oscillatory moving boundary condition

Journal of Differential Equations ◽

10.1016/j.jde.2016.05.029 ◽

2016 ◽

Vol 261 (6) ◽

pp. 3366-3413 ◽

Cited By ~ 1

Author(s):

Yoshiyuki Kagei ◽

Ryouta Oomachi

Keyword(s):

Boundary Condition ◽

Periodic Solution ◽

Half Space ◽

Stokes Equation ◽

Moving Boundary ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Moving Boundary Condition ◽

Time Periodic ◽

Time Periodic Solution

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On the Existence and Stability of Time Periodic Solution to the Compressible Navier–Stokes Equation on the Whole Space

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-015-0902-x ◽

2015 ◽

Vol 219 (2) ◽

pp. 637-678 ◽

Cited By ~ 5

Author(s):

Kazuyuki Tsuda

Keyword(s):

Periodic Solution ◽

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Existence And Stability ◽

Whole Space ◽

Time Periodic ◽

Time Periodic Solution

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On the Spectral Properties for the Linearized Problem around Space-Time-Periodic States of the Compressible Navier–Stokes Equations

Mathematics ◽

10.3390/math9070696 ◽

2021 ◽

Vol 9 (7) ◽

pp. 696

Author(s):

Mohamad Nor Azlan ◽

Shota Enomoto ◽

Yoshiyuki Kagei

Keyword(s):

Spectral Properties ◽

Stokes Equations ◽

Space Time ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Navier Stokes Equations ◽

Infinite Layer ◽

Periodic State ◽

Linearized Problem ◽

Time Periodic

This paper studies the linearized problem for the compressible Navier-Stokes equation around space-time periodic state in an infinite layer of Rn (n=2,3), and the spectral properties of the linearized evolution operator is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the asymptotic expansions of the Floquet exponents near the imaginary axis for the Bloch transformed linearized problem are obtained for small Bloch parameters, which would give the asymptotic leading part of the linearized solution operator as t→∞.

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